Specify one external mailserver

I have one client who demands to keep his "old" mail account with his local ISP, even though the website is hosted on my server. He is either too dumb or too stubborn to change the settings in Outlook Express.

I thought all I would have to do is delete the local MX record and put one in for mail.az.net (his ISP) but that dosen't seem to work.

What would I need to do to get mail bound for donnsboatshop.com (on my server) to his prefered mail provider mail.az.net. The nameserver records (NS1 and NS2) for the site are pointed at my nameservers, so I cant manage the records at the registrar.